Re: [積分] 台大91C

[Fubini (===漂移的阿尼===)]

※ 引述《linda1218 (linda)》之銘言：
:  sqr2
: S  x(sqr(4-x^4))dx =?
:  0

      aqr2
(1/2)S     (sqr(4-x^4))d(x^2)        ( set u=x^2 )
      0

         2
= (1/2) S    sqr(4-u^2) du           (set u=2sina, du=2cosada)
         0

         pi/2
= (1/2) S      4(cosa)^2 da          (by wallis formula)
         0


= 2 (1/2)(pi/2) = pi/2


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推 GBRS:如果不背wallis formula就用半角公式代也行..